Interpolation and Sampling in Spaces of Analytic Functions
The book is based on a series of lectures of the author at the University of Michigan. The topic treated in the book is geometry of interpolating and sampling sequences in Hilbert and Banach spaces of analytic functions on a domain Ω in C. In the first two chapters, the author presents the Carleson theorem and its relation to the Nevanlinna-Pick interpolation. Interpolation and sampling sequences in Bergman spaces are studied in the third chapter. The fourth chapter is devoted to interpolation in the Bloch space and the last two chapters deal with Paley-Wiener spaces. Almost all results in the book are proved. A basic knowledge in the field (complex and functional analysis, basic facts from the Hp and BMO theories) is assumed. The book offers a nice overview of the field.